Select the correct answer.
The length of a rectangle is 3 meters more than the width. The perimeter of the rectangle is 26 meters. If the width is b, which equation represents the situation? How many solutions will this equation have?
A.
(b + 3)(b) = 26, which has one solution
B.
2(b + 3) + 2b = 26, which has infinitely many solutions
C.
2[(b + 3) + b] = 26, which has one solution
D.
2[(b + 3) + b] = 26, which has no solution

Answer:

impossible

Step-by-step explanation:

a denominator can’t be equal to 0. So:

d ≠ 0 ; d ≠ 2

(10 + 4d - 8)/d(d-2) = 5d/ d(d-2)

4d + 2 = 5d

d = 2

But we have said that d can’t be equal to 2, so the equation is impossible.

The required solution after three successive iterations is near x = 7/8. Option c is correct.

Equation is -2x + 6 = -(2/3)^x + 5. Approximate the solution to the equation above using three iterations of successive approximation.

The equation is the values of two expressions that are equal.

Here,

[tex]-2x + 6 = -(2/3)^x + 5[/tex]

Arranging the equation

[tex]-2x + 6 +(2/3)^x - 5 = 0\\(2/3)^x-2x+1=0[/tex]
Since the solution of the equation is when f(x) = 0 at near to  x = 0.8
[tex]f(x) = (2/3)^x-2x+1\\[/tex]

First iteration at x =0.8
[tex]f(0.8) = (2/3)^x-2x+1\\ = (2/3)^{0.8}-2*0.8+1\\ = 0.123[/tex]

It will go up more to get exact zero, so
Second iteration at x = 0.9

[tex]f(0.9) = (2/3)^{0.9}-2*0.9+1\\f(0.9) = -0.106[/tex]

It seems that zero is near 0.9 so will go down
The third iteration at x = 0.87

[tex]f(0.87) = (2/3)^{0.87}-2*0.87+1\\f(0.87) = -0.037[/tex]

Here , solution is much near to x = 0.87 or x =7/8.

Thus, the required solution after three successive iterations is near x = 7/8.

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Answer:

3,375mm^3

Step-by-step explanation:

To find the volume, you do the length times the width times the height. Since this is a cube, the length, width, and height are all 15 mm. Multiply 15 times 15 times 15 to get 3375. The answer is 3375 cubic inches or 3375mm^3

Answer:

a + b = 7

Step-by-step explanation:

a^2 - b^2 = 21

Factor the left side. It is the difference of two squares which factors into the product of a sum and a difference.

(a + b)(a - b) = 21

We are told a - b = 3, so substitute 3 for the factor a - b.

(a + b)(3) = 21

Divide both sides by 3.

a + b = 7

The quotient 35 divided by 11 is the only one among the options that is greater than 3.

To determine which quotient is greater than 3, we can calculate the value of each quotient:

28 divided by 10 = 2.8

35 divided by 11 ≈ 3.182

38 divided by 13 ≈ 2.923

40 divided by 14 ≈ 2.857

Comparing these values, we can see that only the quotient 35 divided by 11, which is approximately 3.182, is greater than 3.

Therefore, the quotient 35 divided by 11 is the only one among the options that is greater than 3.

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Answer:

1,3,4,6

Step-by-step explanation:

Answer: C

Step-by-step explanation:

If you use the quadratic equation you will find that there are two possible answers to this problem

The explanation shows that the equation has exactly two real roots. so the correct option is C.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given that Julie is solving the equation x² + 5x+6= 0 and notices that the discriminant b²- 4ac has a value of 1.

x² + 5x+6= 0

The discriminant = b²- 4ac = 1

It will be Real and distinct because the discriminant is positive.

There are two roots of a quadratic equations always if  the discriminant is positive. We say that the quadratic equation has 2 solution if roots are distinct, and have 1 solutions when both roots are same.

Hence, This tells her that the equation has exactly two real roots. so the correct option is C.

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Answer:

[tex]1 + cot^2 \theta[/tex]

Step-by-step explanation:

Given the expression;

[tex]\frac{tan^2\theta+1}{tan^2 \theta}[/tex]

Separating into partial fraction;

[tex]\frac{tan^2 \theta}{tan^2 \theta} + \frac{1}{tan^2 \theta}\\= 1 + \frac{1}{tan^2 \theta}\\\\[/tex]

Since [tex]\frac{1}{tan \theta} = cot \theta\\[/tex]

Hence the expression becomes;

[tex]1 + cot^2 \theta[/tex]

Answer:

Domain : (-∞, ∞)

Step-by-step explanation:

Domain of a function is a set of x-values of the function.

Therefore, all x-values at which the given function is defined will be the domain of the function.

From the graph attached,

Given function is defined for all x-values.

Domain : Set of all real numbers.

Or Domain : (-∞, ∞)

Answer:

1260

Step-by-step explanation:

5÷100=0.05

0.05×25200=1260

Answer:

n=-2,A

Step-by-step explanation:

15-3n=21

-3n=21-15

-3n=6

n=6/-3

=-2

Answer:

Step-by-step explanation:

as given j=h and k=m then which expression for g is

as from attached image , we can see that its look like two right angle triangle

so from lower triangle we apply the pythagorean theorem .

which state that sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

so small triangle ΔEBD

h² +k²= g²       ---------------(1)

now from big triangle ΔABC

(j + h)² +(m + h)² =f²---------(2)

given j=h and k=m so from equation-2 we can find ,

(h + h)² +(k+ k)² =f²

(2h)² +(2k)²=f²

4h²+ 4k²= f²

4(h²+k²)= f² ----------(3)

now from equation 1 and 3 we can obtained .

4×g² =f²

take square root both side we get,

2×g=f

so g=f/2----- Answer

x = -1

Step-by-step explanation:

[tex] {4}^{5x} = {2}^{2(5x)} = {2}^{10x} [/tex]

[tex] {( \frac{1}{32}) }^{(1 - x)} = {2}^{ - 5(1 - x)} = {2}^{(5x - 5)} [/tex]

or

[tex] {2}^{10x} = {2}^{(5x - 5)} [/tex]

Since both sides have the same base, we can write

10x = 5x - 5

or

5x = -5

x = -1

Answer:

d and e

Step-by-step explanation:

for a

substitute 2 for x

2 + 8 > 14

2 + 8 = 10

10 > 14

10 is not greater than 14 therefore 2 is not a solution to the inequality

for b

substitute 4 for x

4 + 8 > 14

4 + 8 = 12

12 > 14

12 is not greater than 14 therefore 4 is not a solution to the inequality

for c

substitute 6 for x

6 + 8 > 14

6 + 8 = 14

14 > 14

14 is not greater than 14 therefore 6 is not a solution to the inequality

for d

substitute 8 for x

8 + 8 > 14

8 + 8 = 16

16 > 14

16 is greater than 14 therefore 8 is a solution to the inequality

for e

substitute 10 for x

10 + 8 > 14

10 + 8 = 18

18 > 14

18 is greater than 14 therefore 10 is a solution to the inequality

we can conclude that the answers are d and e

Answer:

Ascending order

Step-by-step explanation:

Ascending numbers are numbers that begin from smallest to biggest.

Answer:

$3185

Step-by-step explanation:

Multiply the number of grade 6 students by the money needed ($3.50) and you get 318x3.50=1113

Multiply the number of grade 7 students by the money needed ($3.50) and you get  286x3.50=1001

Multiply the number of grade 8 students by the money needed ($3.50) and you get 306x3.50=1071

Add all the total amounts together and you get $3185

Step-by-step explanation:

everything can be found in the picture

Answer:

It is easier to hammer a sharp nail than a blunt one

Step-by-step explanation:

This is because blunt nail occupies more area than sharped nail. As sharp will exert more pressure as it occupies less area.

Answer:

n = -4

Step-by-step explanation:

[tex](\frac{5}{3} )^2^n^+^1 * (\frac{5}{3} )^5 = (\frac{5}{3})^n^+^2[/tex]

in multiplication if the base are same u can add there exponent.

[tex](\frac{5}{3})^2^n^+^1^+^5 = (\frac{5}{3})^n^+^2[/tex]

base of both sides are equal so their exponent will be equal

2n + 1 + 5 = n + 2

2n + 6 = n + 2

2n - n = 2 - 6

n = -4

Answer:

$28.00

Step-by-step explanation:

1. The markup is 40% of the $20 cost, so the markup is:

(0.40)(20) = 8

2. Then the selling price, being the cost plus markup, is:

20 + 8 = 28

3. The CD set sold for $28.00

Step-by-step explanation:

sp=(100+p)% of cp

=100+40/100*20

=140/100*20

=28

Rewrite 50% as a decimal : 0.50

Multiply the price by 0.50:

18 x 0.50 = 9

The sale price is $9

Answer:

$9

Step-by-step explanation:

price of an item=$18

discount=50%

sale price =? (be x)

sale price= original price -discount% of original price

x=$18 -50/100 * $18

x=$1800-$900/100

=$900/100

=$9

therefore sale price of an item is $9.

Answer:

[tex](x-1)^2 + (y-1)^2 = 10[/tex]

Step-by-step explanation:

From the graph ,

Centre of the circle is (1, 1)

To find radius we find a point through which the circle passes and find the distance between the Centre and the point.

Let that point be (4, 0)

[tex]radius = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2} = \sqrt{(1-4)^2 + (1-0)^2} = \sqrt{10}[/tex]

Equation of the circle :

[tex](x - a)^2 + (y-b)^2 = r^2 \ , \ where \ (a,b)\ is\ the\ centre\ of\ the\ circle\ and\ r\ is\ the\ radius\\\\(x-1)^2 + (y-1)^2 = 10[/tex]

Answer:

10.5 miles

Step-by-step explanation:

[tex]\frac{4\frac{2}{3} }{49} :\frac{1}{y}[/tex]

4 2/3 × y = 1 × 49

[tex]4\frac{2}{3}y=49[/tex]

[tex]4\frac{2}{3}y/4\frac{2}{3} =49/4\frac{2}{3}[/tex]

[tex]y = 10\frac{1}{2}[/tex]

Answer:

-1 ≤ y ≤ 0

Step-by-step explanation:

here, we simply want to know the range of values for sin x over the given interval

The range of values for sin x are simply the values in which y will take over the given interval of x

let’s start with the value sine (-pi)

We have this as;

0

And the value of sin (0) = 0

Recall, between -pi and 0, we have (-pi/2)

so sin (-pi/2) = -1

Thus, we have the correct range of values as;

-1 ≤ y ≤ 0

Answer:

If gas costs $3.75 per gallon and Berto has $12, then he can purchase 12/3.75 gallons. This is approximately 3.2 gallons. So the coordinate on this line would be (3.2, 12).

Actually... It's from web

Answer:

21cm^2

Step-by-step explanation:

Area of Square-Area of semi circles (makes one full circle)

Squares Area = 100

LxW or (10x10)=100

Circle Area = 25/pi

/pi (radius)^2 or /pi(5)^2 = 25/pi

100cm^2-25cm^2 = 21.4601…cm^2 rounded to 21.5 cm^2

The area of the shaded region is 21.5 cm²

'In geometry, a semicircle is a plane figure that is formed by dividing a circle into exactly two parts.'

According to the given problem,

Side length of the square = 10

Area of the square = ( 10 × 10 )

                               = 100 cm²

Now, for the semi-circle,

Diameter = 10 cm

Radius = [tex](\frac{10}{2}[/tex][tex])[/tex] cm

            = 5 cm

Area of the semicircle =  [tex]\frac{\pi r^{2} }{2}[/tex]

                                     = [tex]\frac{\pi * 5^{2} }{2}[/tex]

Since, there are two semicircles in the square, we multiply the area with 2,

⇒ [tex]\frac{\pi *5^{2} }{2}*2[/tex]

= 25[tex]\pi[/tex]

Area of the shaded region = ( 100 - 25π )

                                            = ( 100 - 78.53 )

                                            = 21.46

                                            ≈ 21.5 cm²

Hence, we can conclude, the area of the shaded region is 21.5 cm².

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Answer:

∠EFG=2×∠EHG

∠EFG=2×42

∠EFG=84°

so,m∠EFG=84°

------------------------

hope it helps...

have a nice day!!

Answer:

x =62

Step-by-step explanation:

The two angles form a straight line so they add to 180

x+118 = 180

Subtract 118 from each side

x = 180-118

x =62

Answer:

x = 62°

Step-by-step explanation:

These both angles are located at straight line.

So, the sum of both angles is 180 °.

x + 118 ° = 180 °

Subtract 118 ° from 180 °

x = 180 ° - 118 °

x = 62 °

Answer:

x = 5.5 (rounded)

Step-by-step explanation:

Equation: 700 = 132.69x - 25.96

Add 25.96 to both sides: 700+25.96 = 132.69x -25.96 + 25.96

Simplify: 725.96 = 132.69x

Isolate x

Divided both sides by 132.69: [tex]\frac{725.96}{132.69} = \frac{132.69x}{132.69}[/tex]

Simplify: x = 5.5 (rounded)